please solve and show process X: In engineering, weights of people are considere

Question

please solve and show process

X: In engineering, weights of people are considered so that airplanes and elevators aren't overloaded, chairs won't break and other embarrassing things won't occur. Men's weights are normal with a mean of 173 lbs., and a standard deviation of 30 lbs. a. What is the distribution for a single mans weight? b. What is the probability a randomly selected man weighs more than 180 lbs.? c. What is the distribution of the average men's weight if we are considering a SRS of 9 men? d. If 9 men are randomly selected (say to be in an elevator), what is the probability that their average weight is more than 180 lbs

Explanation / Answer

a) distribution fo single men weight is normal with population mean =173 and std deviation is 30

b) probability that weight is more then 180 lbs =P(X>180)=1-P(X<180)=1-P(Z<(180-173)/30)

=1-P(Z<0.2333)=1-0.5922 =0.4078

c) for population is normally distirbution therefore sampling distirbution of sample mean of 9 men is normal with

mean weight =180

and std error of mean =std deviation/(n)1/2 =30/(9)1/2 =10

d)  probability that average weight is more then 180 lbs =P(Xbar>180)=1-P(Xbar<180)=1-P(Z<(180-173)/10)

=1-P(Z<0.7)=1-0.7580 =0.2420

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